Готові списки джерел за темами / Suzuki-Trotter method

Добірка наукової літератури з теми "Suzuki-Trotter method"

Автор: Grafiati

Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Suzuki-Trotter method"

Wijesinhe, H. S., and K. A. I. L. Wijewardena Gamalath. "Spin Waves in Two and Three Dimensional Magnetic Materials." International Letters of Chemistry, Physics and Astronomy 49 (April 2015): 35–47. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.49.35.

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The equations of motion for the dynamic properties of spin waves in three dimensions were obtained using Heisenberg model and solved for two and three dimensional lattices analytically up to an exponential operator representation. The second order Suzuki Trotter decomposition method was extended to incorporate second nearest interaction parameters into the numerical solution. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for two dimensional lattice as well as three dimensional simple cubic and bcc lattices. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor presenting the variation of energy transfer with respect to momentum transfer of spin waves. Second order Suzuki Trotter algorithm used conserved the energy.

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Wijesinhe, H. S., and K. A. I. L. Wijewardena Gamalath. "Spin Waves in Two and Three Dimensional Magnetic Materials." International Letters of Chemistry, Physics and Astronomy 49 (April 7, 2015): 35–47. http://dx.doi.org/10.56431/p-7562a7.

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Tranter, Andrew, Peter J. Love, Florian Mintert, Nathan Wiebe, and Peter V. Coveney. "Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure." Entropy 21, no. 12 (December 13, 2019): 1218. http://dx.doi.org/10.3390/e21121218.

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Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.

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MIYASHITA, Seiji, and Tota NAKAMURA. "MONTE CARLO STUDIES ON FRUSTRATED QUANTUM SPIN SYSTEMS BY A NEW APPROACH TO THE NEGATIVE-SIGN PROBLEM: TRANSFER-MATRIX MONTE CARLO METHOD." International Journal of Modern Physics C 07, no. 03 (June 1996): 425–31. http://dx.doi.org/10.1142/s0129183196000375.

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A new technique for the negative sign problem in the quantum Monte Carlo method using the Suzuki-Trotter decomposition is introduced. In order to reduce the cancellation between between samples with positive and negative weights, we make use of the transfer matrix method, which has been named the Transfer-Matrix Monte Carlo method. Applications to the Heisenberg antiferromagnet on the ∆-chain and on the kagome lattice, and also to the Kondo lattice system also are given.

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LANDAU, D. P., SHAN-HO TSAI, M. KRECH, and ALEX BUNKER. "IMPROVED SPIN DYNAMICS SIMULATIONS OF MAGNETIC EXCITATIONS." International Journal of Modern Physics C 10, no. 08 (December 1999): 1541–51. http://dx.doi.org/10.1142/s0129183199001327.

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Using Suzuki–Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special cases, also conserve the energy and maintain time reversibility. We investigate integration schemes of up to eighth order and show that these new algorithms can be used with much larger time steps than a well established predictor–corrector method. These methods may lead to a substantial speedup of spin dynamics simulations, however, the choice of which order method to use is not always straightforward.

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Henneke, Felix, and Manfred Liebmann. "A generalized Suzuki–Trotter type method in optimal control of coupled Schrödinger equations." Computing and Visualization in Science 17, no. 6 (December 2015): 277–93. http://dx.doi.org/10.1007/s00791-016-0266-2.

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Ariasoca, Thomas Aquino, Sholihun, and Iman Santoso. "Trotter-Suzuki-time propagation method for calculating the density of states of disordered graphene." Computational Materials Science 156 (January 2019): 434–40. http://dx.doi.org/10.1016/j.commatsci.2018.10.016.

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Hutchinson, J., J. P. Keating, and F. Mezzadri. "On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems." Advances in Mathematical Physics 2015 (2015): 1–18. http://dx.doi.org/10.1155/2015/652026.

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We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.

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Paraniak, Mikołaj M., and Berthold-Georg Englert. "Quantum Dynamical Simulation of a Transversal Stern–Gerlach Interferometer." Symmetry 13, no. 9 (September 8, 2021): 1660. http://dx.doi.org/10.3390/sym13091660.

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Originally conceived as a thought experiment, an apparatus consisting of two Stern–Gerlach apparatuses joined in an inverted manner touched on the fundamental question of the reversibility of evolution in quantum mechanics. Theoretical analysis showed that uniting the two partial beams requires an extreme level of experimental control, making the proposal in its original form unrealizable in practice. In this work, we revisit the above question in a numerical study concerning the possibility of partial-beam recombination in a spin-coherent manner. Using the Suzuki–Trotter numerical method of wave propagation and a configurable, approximation-free magnetic field, a simulation of a transversal Stern–Gerlach interferometer under ideal conditions is performed. The result confirms what has long been hinted at by theoretical analyses: the transversal Stern–Gerlach interferometer quantum dynamics is fundamentally irreversible even when perfect control of the associated magnetic fields and beams is assumed.

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Wijesinhe, H. S., and K. A. I. L. Wijewardena Gamalath. "Spin Waves in One Dimensional Magnetic Material." International Letters of Chemistry, Physics and Astronomy 47 (February 2015): 24–39. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.47.24.

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Анотація:

Using Heisenberg model, the equations of motion for the dynamic properties of spin waves in three dimensions were obtained and solved analytically up to an exponential operator representation. Second order Suzuki Trotter decomposition method with evolution operator solution was applied to obtain the numerical solutions by making it closer to real spin systems. Computer based simulations on systems in micro canonical ensembles in constant-energy states were used to check the applicability of this model for one dimensional lattice by investigating the occurrence, temperature dependence and spin-spin interaction dependence of the spin waves. A visualization technique was used to show the existence of many spin wave components below the Curie temperature of the system. In the magnon dispersion curves all or most of the spin wave components could be recognized as peaks in the dynamic structure factor. Energy conservation of the algorithm is also shown.

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Більше джерел

Частини книг з теми "Suzuki-Trotter method"

Coolen, Anthony C. C., Theodore Nikoletopoulos, Shunta Arai, and Kazuyuki Tanaka. "Dynamical Analysis of Quantum Annealing." In Sublinear Computation Paradigm, 295–317. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-4095-7_12.

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AbstractQuantum annealing aims to provide a faster method than classical computing for finding the minima of complicated functions, and it has created increasing interest in the relaxation dynamics of quantum spin systems. Moreover, problems in quantum annealing caused by first-order phase transitions can be reduced via appropriate temporal adjustment of control parameters, and in order to do this optimally, it is helpful to predict the evolution of the system at the level of macroscopic observables. Solving the dynamics of quantum ensembles is nontrivial, requiring modeling of both the quantum spin system and its interaction with the environment with which it exchanges energy. An alternative approach to the dynamics of quantum spin systems was proposed about a decade ago. It involves creating stochastic proxy dynamics via the Suzuki-Trotter mapping of the quantum ensemble to a classical one (the quantum Monte Carlo method), and deriving from this new dynamics closed macroscopic equations for macroscopic observables using the dynamical replica method. In this chapter, we give an introduction to this approach, focusing on the ideas and assumptions behind the derivations, and on its potential and limitations.

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